1. Prepare the Custard Filling

In a medium saucepan, whisk together granulated sugar and cornstarch, ensuring there are no lumps. Gradually pour in the whole milk, whisking continuously until the mixture is smooth. Place the saucepan over medium heat, stirring constantly until the mixture thickens and begins to bubble, which should take about 5-7 minutes. Lower the heat and temper the egg yolks by slowly whisking in a few spoonfuls of the hot milk mixture. Once tempered, pour the yolk mixture back into the saucepan. Cook the custard over low heat, stirring constantly, until it reaches a thick, pudding-like consistency, about 3-4 minutes. Remove the saucepan from heat and stir in the butter and vanilla extract until smooth. Allow the custard to cool slightly before assembling the pie.

2. Layer the Bananas and Custard

Arrange a layer of sliced bananas at the bottom of the pre-baked pie crust. Pour half of the custard filling over the bananas, smoothing it out with a spatula. Add another layer of banana slices, followed by the remaining custard, ensuring an even spread.

3. Chill the Pie

Cover the pie with plastic wrap, pressing it gently against the custard to prevent a skin from forming. Refrigerate the pie for at least 3 hours, or until completely set.

4. Add the Topping and Serve

Before serving, generously top the pie with whipped cream. For a decorative finish, add extra banana slices, a sprinkle of cinnamon, or even chocolate shavings.